2D Geometry Questions and Answers

8 Triangle MNT has the following measurements ZM 45 21 75 a Make a rough sketch of this triangle b Use your ruler and protractor to carefully draw the triangle c Determine the area of your triangle You may need to make additional measurements d Determine the perimeter of your triangle You may need to make additiona measurements MT 6 4 cm

Name all similar triangles to triangle CDE A w C 55 15 90 F 17 B D

Segment VU is parallel to segment LM Find the missing length L V M24 U 44 27 24 11 8 N

AL B 1 6m 1 2m A ramp is prism shown 95 Find the length Find DCE

2 1 3 5 2 22 23 3 23 24 4 21 24 6 1 21 and 22 are complementary 2 mz1 m22 V Given 21 and 22 are complementary Prove XA1 XC 3 mz AXC mz1 mz2 4 mz AXC 5 ZAXC is a right angle 3 4 Skip this step 4 1 2 3 VI Given 21 and 22 are supplementary Prove 23 and 24 are supplementary 4 5 6 1 Given 2 Def of supplementary angles 3 Vertical angles are congruent 4 Def of congruent angles 5 Substitution 6 Def of

Describe and graph the set of points that satisfies the given equation in R xyz space x 2 2 z 5 2 4

Graph the image of the figure using the transformation given 1 translation 2 3 3 reflection across the y axis 5 translation r y 5 4 2 translation 4 5 4 reflection across the x axis 6 translation x y x y 4

Write the equation from the following table BE SURE TO IDENTIFY THE SLOPE AND Y INTERCEPT X 3 0 3 6 y 3 1 5 9

Normal Find the x and y intercepts for the equation BE SURE TO WRITE AS COORDINATE POINTS 12x 6y 108

7 Trapezoid ABCD has the following measurements The bases are AD and BC ZA 67 AD 10 4 cm D 90 DC 5 0 cm a Make a rough sketch of this trapezoid The bases of a trapezoid are the parallel sides b Use your ruler and protractor to carefully draw trapezoid ABCD Measure sides AB and BC and ZB

Solve for x The pair of polygons are similar 60 10x 21 O 12 O 14 110 O 17 54

yard is at point B with the top of the tree at point C Sue stand so her shadow meets the end of the tree s shadow a point A A 5 ft 8 ft D Question 4 24 ft B What is the ratio of the triangles 1 p

The two polygons are similar Find the measure of angle E A 6 12 70 50 90 60 B 75 D E None of the other answers are correct H 125 G

Triangles ABC and EDC are similar Find the measure of angle D 62 B O 62 O 61 O 67 O 60 610 D E

The two polygons are similar Find the values of x and y X y 22 60 18 W x 4 12

Solve for x The pair of polygons are similar 5x 5 B O 15 The scale factor from A to B is 9 10 O 18 O 19 A O22 72

The two polygons shown are similar Calculate the value of OK M OK ok H R 17 12 75 S

A passenger in an airplane flying at an altitude of 12 miles sees two towns directly to the left of the plane The angles of depression to the towns are 26 and 45 How far apart are the towns Round to two decimal places as needed Show your work here

In parallelogram DEFG DH x 3 HF 3y GH 4x 5 and HE 2y 3 Find the values of x and y The layan G OA OB OC OD x H R 2 y 3 x 6 y 3 x 3 y 2 x 3 y 6

For the parallelogram if m42 5x 28 and m44 3x 10 find m43 The diagram is not to scale OA 163 OB 17 173 9 C D 1

Classify the quadrilateral OA square OB parallelogram OC rhombus OD trapezoid

Three angles in a quadrilateral measure 54 25 and 99 What is the measure of the fourth angle OA 2 OB 92 C 182 272

For a triangle list the respective names of the points of concurrency C perpendicular bisectors of the sides bisectors of the angles medians lines containing the altitudes A circumcenter incenter orthocenter centroid OB OC OD circumcenter incenter centroid orthocenter incenter circumcenter orthocenter centroid incenter circumcenter centroid orthocenter

The OA incenter OB circumcenter OC median OD concurrent of a triangle is a segment whose endpoints are a vertex and the midpoint of the opposite side

3 and M are base angles of isosceles trapezoid JKLM If m43 20x 9 and m M 14x 15 find m K OA 151 OB C 1 29 75 5

Find the length of segment AB given that segment DB is a median of the triangle and AC 26 B OA 26 OB 52 OC Not enough information is given OD 13

Find the center of the circle that you can circumscribe about the triangle A 4 1 5 c 4 3 OA OB OC D B 2 3 0 1 21 13 0 2 1 1 4 5 X

One side of a kite is 8 cm less than four times the length of another side The perimeter of the kite is 78 cm Find the lengths of the sides of the kite DA 9 4 cm and 29 6 cm OB 23 5 cm and 86 cm OC 23 5 cm OD 9 4 cm

Name the median for AQRS OA B OC QV RT QT SU

MO bisects LLMN m LM0 8x 23 and m NMO 2x 37 Solve for x and find m LMN The diagram is not to scale OA OB OC SOD x 9 m LMN 98 x 9 m LMN 49 x 10 m LMN 114 x 10 m LMN 57 L 0 M N

6 For which situation could you prove A1 A2 using the HL Theorem I 2 OA I only OB I and II OC II and III OD II only II 4 8 III 2

MO bisects LMN m LMN 5x 23 and m4LMO x 32 Find m NMO The diagram is not to scale L OA OB C D 66 45 75 61 29 M N

Find the value of x The diagram is not to scale 48

1 The triangles CER and LUR are C E R OA Congruent by HL OB Congruent by SAS OC Congruent by AAS OD Not necessarily congruent

Given XY ZW and ZY WX State which postulate or theorem you can use to prove that the triangles are congruent How can you use this to prove that Y W W Z OA AAS Corresponding parts of congruent triangles are congruent OB ASA Corresponding parts of congruent triangles are congruent OC SSS Corresponding parts of congruent triangles are congruent OD SAS Corresponding parts of congruent triangles are congruent

The triangles below are congruent by A A SAS AAS HL

3 What other information do you need in order to prove the triangles congruent using the SAS Congruence Postulate B C D OA ZBAC ELDAC OB AB AD C AB AD D LCBA LCDA 2

Use the information in the figure 2D measures D 116 E F Drawing not to scale degrees

The triangles are congruent by the AABD ACBD B congruence theorem SSS SAS ASA

What other information do you need in order to prove the triangles congruent using the SAS Congruence Postulate B C D OA AC BD OB ZBAC ZDAC OC ZCBA CDA OD AC1 BD

4 A triangular plot of land has three sides one measures 110 feet and another measures 215 feet The angle between these two sides is 65 a Draw a rough sketch of this plot of land You do not need to measure this sketch but you should try to make the 215 foot side about twice as long as the 110 foot side Also try to make the angle close to 65 b Decide on a scale Look at your longest measurement Try to make your drawing fill about half a page Write the scale in a box on your drawing Note If you are having trouble deciding on a scale read example 1 c Convert all the real measurements using your scale d Use a ruler and protractor to make a scale drawing Label all sides with their ruler measurements and in parentheses the real world measurements Label angle measurements as well e Measure the third side of the triangle in your scale drawing How long is the third side of the lot

Andrew is proving that AJKL AMNO given LKJL ZNMO and ZKLJ ZNOM He has already MO determined that a dilation with scale factor JL will map AJKL onto AJ K L where J L MO Which congruence criterion should Andrew use to show that AJ K L AMNO SSS SAS ASA M AAS

State if the pair of triangles are similar If so state how you know they are similar and complete the similarity statement 828 804 Q 1120 not similar AQRS 1151 similar SAS similarity ACDQ similar AA similarity ACDQ similar SSS similarity ACDO R

Calculate the volume of an object with dimensions measuring 12 cm x 3 cm x 9 cm 21cm3

M A P N In Rhombus LMNO angle LMN measures 31 20 degrees what is the measure of angle MNO Type your answer

The diagonal of a square is 381 What is the length of a side

Solve For Angle A B 11 9 7 10 10

The total cost of being a member of Grenoble Soccer Club is represented by y 20x 150 where y is the Total Cost for club membership and x is the months you have been at the club Call this equation Line 1 The total cost of being a member of East York Soccer Club is represented by y 30x 100 where y is the Total Cost S for club membership and x is the months you have been at the club Call this equation Line 2 190 180 300 290 280 270 260 250 240 230 220 210 200 170 160 150 140 130 10 20 120 110 100 90 80 70 60 50 40 30 20 10 Find the point of intersection of the lines Use one method to solve Option A Solve this Linear System by graphing Graph the two equations on one grid one graph with two lines Label each axis Label the intersection point on the graph

the angle of elevation theta of the sun and sky at any latitude L is calcuclated with the formula sin theta cos d cos I cos w sin D sin L W is the number of raidans the earth has roated through since noon when W 0 D is the declination of the sun westville has a latitude of 35 8 degrees find the angle of elevation theta in degrees of the sun at 3pm on febuary 29 2012 Where at that tine D 0 1425 and w 0 7854

Match the notation with the term that best describes it D HF ZBAD AB G LFGE AB AD E F E 1 Radius 2 Diameter 3 Secant 4 Chord 5 Tangent 6 Center 7 Point of tangency 8 Central Angle 9 Inscribed Angle